Question

Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought four notebooks and five thumb drives for $\backslash (116$. Lisa bought two notebooks and three thumb dives for $\backslash )68$. Find the cost of each notebook and

each thumb drive.

Short answer

The cost of each notebook is$\$4$and the cost of each thumb drive is$\$20$

Step-by-step solution

Step 1. Given 

Troy bought $4$notebooks and $5$thumb drives for $\$116$.

Lisa bought $2$notebooks and $3$thumb drives for$\$68$

Step 2. Form the linear equations

Let $x$denote the costa of each notebook and$y$denote the cost of each thumb drive.

$4$notebooks and $5$ thumb drives bought for$\$116$

$4x+5y=116$

$2$notebooks and $3$thumb drives bought for $\$68$

$2x+3y=68$

Step 3. Solve the linear equations

Solve the system of linear equations.

$4x+5y=116$

$2x+3y=68$

Solve the second equation for $x$,

$2x=68-3y$

Divide both sides by $2$,

$x=34-\frac{3}{2}y$

Step 4. Solve for y

Substitute $x=34-\frac{3}{2}y$in the first equation, we get,

$4x+5y=116$

$4(34-\frac{3}{2}y)+5y=116$

$136-6y+5y=116$

$136-y=116$

$y=136-116$

$y=20$

The cost of each thumb drive is$\$20$

Step 5. Solve for x

Substitute $y=20$in the first equation, we get,

$4x+5y=116$

$4x+5\left(20\right)=116$

$4x+100=116$

$4x=16$

Divide both sides by $4$,

$x=4$

The cost of each notebook is$\$4$

Step 6. Check the answer

Substitute $x=\$4$,

$y=\$20$in the first equaton,

$4x+5y=\$116$

$4(\$4)+5(\$20)=\$116$

role="math" localid="1644343748957" $\$16+\$100=\$116$

$\$116=\$116$

Hence the equation holds true.